Analytically evaluating the influence of crack on the mesh stiffness of a planetary gear set

a b s t r a c t
Article history:
Received 19 February 2013
Received in revised form 3 February 2014
Accepted 3 February 2014
Available online 2 March 2014
Time-varying mesh stiffness, caused by the change of tooth contact number and contact position,
is one of the main sources of vibration of a gear transmission system. In order to comprehensively
understand the vibration properties of a planetary gear set, it is necessary to evaluate the mesh
stiffness effectively. When a crack happens in one gear, the mesh stiffness will decrease and
consequently the vibration properties of the gear systemwill change. This change of vibration can
be characterized through dynamic simulation of a gearbox and processed further to detect the
crack severity and location. In this paper, the potential energy method is used to analytically
evaluate the mesh stiffness of a planetary gear set. A modified cantilever beam model is used to
represent the external gear tooth and derive the analytical equations of the bending, shear and
axial compressive stiffness. A crack propagation model is developed and the mesh stiffness
reduction is quantified when a crack occurs in the sun gear or the planet gear.